High resolution algorithms for multidimensional population balance equations

TLDR

Population balance equations have been used to model a wide range of processes including polymerization, crystallization, cloud formation, and cell dynamics. The study proposes adapting high‑resolution finite volume methods from compressible gas dynamics to solve population balance equations. The authors implement high‑resolution finite volume algorithms—originally developed for compressible gas dynamics—into the ParticleSolver package to simulate multidimensional population balance equations with nucleation and size‑dependent growth rates in batch and continuous processes. The algorithms deliver markedly higher numerical accuracy for sharp distributions while reducing computational cost by orders of magnitude compared to conventional finite difference and finite volume methods. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2738–2749, 2004.

Abstract

Abstract Population balance equations have been used to model a wide range of processes including polymerization, crystallization, cloud formation, and cell dynamics. Rather than developing new algorithms specific to population balance equations, it is proposed to adapt the high‐resolution finite volume methods developed for compressible gas dynamics, which have been applied to aerodynamics, astrophysics, detonation waves, and related fields where shock waves occur. High‐resolution algorithms are presented for simulating multidimensional population balance equations with nucleation and size‐dependent growth rates. For sharp distributions, these high‐resolution algorithms can achieve improved numerical accuracy with orders‐of‐magnitude lower computational cost than other finite difference and finite volume algorithms. The algorithms are implemented in the ParticleSolver software package, which is applied to batch and continuous processes with one and multiple internal coordinates. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2738–2749, 2004